Original battery died sometime last year, been putting off getting a replacement ever since. Happy to report a solid 7-10h from the ifixit brand. I forgot how nice being actually cordless is! :
PSP 2000 Repair - iFixit
PSP Go Teardown - iFixit
PSP Go Start and Select Button Replacement. This is how it's done. I'm surprised how there is no guide on this. Not even on iFixIt. : r/PSP